It follows the US Company’s failed attempt to block sales of the South Korean firm’s Galaxy Tab tablets.
Apple has not commented on the news.
The order did not feature in Judge Colin Birss’s judgment published on 9 July, but Bloomberg said the matter was discussed in the court following the verdict.
It said the notices must make reference to the court case and should be designed to “correct the damaging impression” that Samsung’s tablets had aped the look of Apple’s products.
“They do not have the same understated and extreme simplicity which is possessed by the Apple design,” said the judge at the time.
“They are not as cool. The overall impression produced is different.”
However, the judge refused Samsung’s request that Apple be forbidden from restating its claim that its design rights had been infringed.
Judge Birss said that the US firm was “entitled” to hold the opinion that his judgement was wrong.
A statement from Samsung said: “Should Apple continue to make excessive legal claims based on such generic designs, innovation in the industry could be harmed and consumer choice unduly limited.”